No. 4 Murray, off to a 20-1 start his year, has won six of eight matches overall against No. 2 Federer.
Murray, a 21-year-old Scot, will face the winner of the semifinal between No. 1 Rafael Nadal and No. 7 Andy Roddick.
The 27-year-old Federer, whose four-year stint at No. 1 ended last year, made some outstanding shots against Murray, and some awful ones. Inconsistency remains his problem as he tries to fight his way back to the top.
The Swiss star made a whopping 32 unforced errors, including several by clanging routine shots off the frame of his racket. Murray was a model of consistency, scrambling back and forth to keep the ball in play and making just 15 unforced errors.
After Federer came back to win the second set, Murray earned a break in the fourth game of the third to take control. Murray had a scary moment in that game when his feet slipped out from under him and he did the splits while trying to stop, turn and get to a shot behind him. He yelled in pain, but got up off the court a few seconds later and obviously wasn't hampered - he won the next three points.
Murray, the only player who did not lose a set on his way to the semis, is trying for his third title of the season. He won at Dubai and Rotterdam.
Vera Zvonareva, who defeated Victoria Azarenka in the women's semis, joined with Azarenka to win the women's doubles title, beating Gisela Dulko and Shahar Peer 6-4, 3-6, 10-5 (super tiebreaker).
Zvonareva will face defending champion Ana Ivanovic for the singles championship.
Both the men's and women's singles finals are Sunday.
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